Abstract
In this paper, we present two fast learning neural network classifiers with a single hidden layer: the ‘Phase Encoded Complex-valued Extreme Learning Machine (PE-CELM)’ and the ‘Bilinear Branch-cut Complex-valued Extreme Learning Machine (BB-CELM)’. The proposed classifiers use the phase encoded transformation and the bilinear transformation with a branch-cut at 2π as the activation functions in the input layer to map the real-valued features to the complex domain. The neurons in the hidden layer employ the fully complex-valued activation function of the type of a hyperbolic secant function. The parameters of the hidden layer are chosen randomly and the output weights are estimated as the minimum norm least square solution to a set of linear equations. The classification ability of these classifiers are evaluated using a set of benchmark data sets from the UCI machine learning repository. Results highlight the superior classification ability of these classifiers with least computational effort.
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References
Kim, T., Adali, T.: Fully-complex multilayer perceptron network for nonlinear signal processing. Journal of VLSI Signal Processing 32(1-2), 29–43 (2002)
Li, M.B., Huang, G.B., Saratchandran, P., Sundararajan, N.: Fully complex extreme learning machines. Neurocomputing 68(1-4), 306–314 (2005)
Savitha, R., Suresh, S., Sundararajan, N., Saratchandran, P.: A new learning algorithm with logarithmic performance index for complex-valued neural networks. Neurocomputing 72(16-18), 3771–3781 (2009)
Savitha, R., Suresh, S., Sundararajan, N.: A fully complex-valued radial basis function network and its learning algorithm. International Journal of Neural Systems 19(4), 253–267 (2009)
Savitha, R., Suresh, S., Sundararajan, N.: A self-regulated learning in fully complex-valued radial basis function networks. In: Proc. of International Joint Conference on Neural Networks, IJCNN 2010 (2010)
Nitta, T.: The computational power of complex-valued neuron. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 993–1000. Springer, Heidelberg (2003)
Nitta, T.: On the inherent property of the decision boundary in complex-valued neural networks. Neurocomputing 50, 291–303 (2003)
Nitta, T.: Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Networks 16(8), 1101–1105 (2003)
Aizenberg, I., Moraga, C.: Multilayer feedforward neural network based on multi-valued neurons (MLMVN) and a backpropagation learning algorithm. Soft Computing 11(2), 169–193 (2007)
Amin, M.F., Murase, K.: Single-layered complex-valued neural network for real-valued classification problems. Neurocomputing 72(4-6), 945–955 (2009)
Amin, M.F., Islam, M.M., Murase, K.: Ensemble of single-layered complex-valued neural networks for classification tasks. Neurocomputing 72(10-12), 2227–2234 (2009)
Blake, C., Merz, C.: UCI Repository of Machine Learning Databases, Department of Information and Computer Sciences, University of California, Irvine (1998), http://archive.ics.uci.edu/ml/
Suresh, S., Omkar, S.N., Mani, V., Guru Prakash, T.N.: Lift coefficient prediction at high angle of attack using recurrent neural network. Aerospace Science and Technology 7(8), 595–602 (2003)
Lu, Y., Sundararajan, N., Saratchandran, P.: A sequential learning scheme for function approximation using minimal radial basis function neural networks. Neural Computation 9(2), 461–478 (1997)
Huang, G.-B., Saratchandran, P., Sundararajan, N.: An efficient sequential learning algorithm for growing and pruning RBF (GAP-RBF) networks. IEEE Transactions on System, Man and Cybernetics B 34(6), 2284–2292 (2004)
Liang, N.-Y., Huang, G.-B., Saratchandran, P., Sundararajan, N.: A fast and accurate on-line sequential learning algorithm for feedforward networks. IEEE Transactions on Neural Networks 17(6), 1411–1423 (2006)
Cristianini, N., Taylor, J.S.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Suresh, S., Dong, K., Kim, H.J.: A sequential learning algorithm for self-adaptive resource allocation network classifier. Neurocomputing 73(16-18), 3012–3019 (2010)
Suresh, S., Venkatesh Babu, R., Kim, H.J.: No-reference image quality assessment using modified extreme learning machine classifier. Applied Soft Computing 9(2), 541–552 (2009)
Suresh, S., Sundararajan, N., Saratchandran, P.: A sequential multi-category classifier using radial basis function networks. Neurocomputing 71(7-9), 1345–1358 (2008)
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Savitha, R., Suresh, S., Sundararajan, N., Kim, H.J. (2011). Fast Learning Fully Complex-Valued Classifiers for Real-Valued Classification Problems. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21105-8_70
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DOI: https://doi.org/10.1007/978-3-642-21105-8_70
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